500 students
.
73 students study all three subjects
97 study chemistry and physics, but we have already counted 73 of them, leaving an additional 24 students
65 students study only physics and biology (138-73)
79 students study only chemistry and biology (152-73)
At this point 176 students study chemistry, meaning 104 students study only chemistry (280-176)
162 already study physics, meaning 92 students study only physics (254-162)
217 already study biology, leaving 63 students who study only biology (280-63)
Total students is then 73 + 24 + 65 + 79 + 104 + 92 + 63 = 500